This is not entirely implausible as a portrayal of slavery. When white children were raised by slaves, they can grow to love them even as they feel they are inferior... you loved your puppy as a child, no doubt.
Stephen raised him as a boy, and was always a mentor figure. Calvin no doubt grew to rely on him for advice and wisdom, and those would be no less valuable when he became a man. Stephen then became Calvin's own steward, and after years of doing this job well no one would come to doubt that Stephen spoke with Calvin's authority when giving commands.
In the immediate aftermath of Calvin's death (and with Stephen having no blame in it, trying to prevent it and afterwards trying to avenge it), they couldn't instantly stop listening to the man... ingrained habits might take hours or days to be questioned. Especially so if they agreed with the commands being given (which they might very well agree with). Stephen was never giving orders to be lenient or kind to Django, after all.
Also if there were cause for future embarrassment (someone gossips that they were being ordered around by a negro), this could readily be denied.
These are tropes that go beyond just American slavery... in the Roman Republic/Empire, slaves often rose to high status and were respected... no one would refuse advice/orders to be spiteful, knowing that the immediate gratification would be outweighed by the long term disadvantage.
